Contents Online
Mathematical Research Letters
Volume 22 (2015)
Number 1
Deformation by cocycles of pointed Hopf algebras over non-abelian groups
Pages: 59 – 92
DOI: https://dx.doi.org/10.4310/MRL.2015.v22.n1.a5
Authors
Abstract
We explore a method for explicitly constructing multiplicative $2$-cocycles for bosonizations of Nichols algebras $\mathfrak{B}(V)$ over Hopf algebras $H$. These cocycles arise as liftings of $H$-invariant linear functionals on $V \otimes V$ and give a formula for deforming braided-commutator-type relations. Using this construction, we show that all known finite-dimensional pointed Hopf algebras over the dihedral groups $\mathbb{D}_m$ with $m = 4t \geq 12 \,$, over the symmetric group $\mathbb{S}_3$, and some families over $\mathbb{S}_4$ are cocycle deformations of bosonizations of Nichols algebras.
2010 Mathematics Subject Classification
16T05
Published 13 April 2015